Solve for x. number 1) -3x=27. Number 2) 3/7x=15.?

Question

Please help!! and please explain how to do this, i dont understand the examples in the book.

Answer 1

let's do no.1. -3x = 27. think about this in a common sense. x , which is a something, multiplies with -3 to give +27. to get the positive number, the x has to be a minus.
so, the 'x' must have a minus sign.
than, just consider the numbers 3 x 'x' = 27. and, you know that 3 x 9 = 27. so, x is 9 and from previous conclusion, x is minus.
So, the right answer is minus nine (-9).

to think it with a maths point of view, x is multipled with minus three. to get rid of three, you have to divide both sides with three.
this gives you ==> -x = 27/3.
and you know that 27/3 is 9!
so, you got ==> -x = 9.
so , to remove minus sign from x , you multiply both sides with minus one s0, (-1) x (-x) = (-1)x(-9).
so you got x= -9. got it.

the other answer is hard to think from common sense point. so better stick to algebraic method.You must prefer algebraic method in order to extend your knowledge in mathematics.

So, the answer is 1/35.
similar to the first one, multiply both sides with 1/7x. so, you get ==> 3= 15 x 7x. and, divide both sides with 15 and you get ==> 1/5 = 7x. so, divide 1/5 with 7 and you get 1/35!

Answer 2

Generally, to solve equations, you want to "undo" the equation. As long as you do the same thing to both sides, you'll be fine :)

1) This is an equation with multiplication. (-3x means -3 times x). So, you need to divide both sides by -3 to "undo" the multiplication.

-3x divided by -3 is just x.

27 divided by -3 is -9. So, after dividing both sides by -3, x=-9 is what's left. When x is by itself on one side, that's your answer.

2) This is also a mult. problem. 3/7 times x. So, to undo that, divide both sides by 3/7. 15 divided by 3/7 is a bit tricky. A trick for dividing by fractions is to multiply by the reciprocal (flip the fraction). So, 15 divided by 3/7 is the same as 15 multiplied by 7/3. That's 35. So, your answer is x=35.



***The reason that you're getting two different answers for #2 is because people are giving you the answers for two different problems. If your original problem is (3/7) * x = 15, then the answer is 35. If your original problem is 3/(7*x) = 15 (the x is in the denominator), then the answer is 1/35.

Answer 3

1) -3x=27

divide both sides by -3 so x is all by itslef

-3x/-3 = 27/-3
x=-9

2) 3/7x=15 not (3/7)x = 15
(The procedure below solves for the equation as shown. If it is supposed to be (3/7)x = 15, this is not the correct procedure or answer but the method used applies)

multiple both sides by 7x to get rid of the fraction

(3/7x)(7x) =15(7x)
3 = 105x

divide both sides by 105 to get x alone

3/105 = 105x/105
3/105 = x
reduce the fraction
1/35 = x
x=1/35

note that 3/7 x 7/3 = 1


if its (3/7)x = 15

mult both sides by 7/3
(3/7)(x)(7/3) = (15)(7/3)
x = (105)/(3)
x = 35

Answer 4

see its -3x=27 then -3 will divide 27 and u get -9
therefore x=-9

2) 3/7x=15 when 3/7 goes on the other side of the = sign it inverts and becomes 7/3 tht u can multiply with 15 or even divide 15 by 3/7 to get x=35
basic funda is to isolate x and take all the terms on one side of the = sign to get the ans for x

Answer 5

1) -3x=27
divide both sides of the = sign by -3 and you get

x=27/-3 which simplifies to x= -9

2) 3/7x=15
here you multiply each side by 7/3 and you get

x=15 (7/3) you simplify by multiplying 15/1 times 7/3

you do that by multiplying 15 x 7 and 3 x 1 which gives you
x=105/3
simplyfied x=35

Answer 6

1. x=6
2. X=9

Answer 7

well you're getting the answers so I'll explain how to do it.

If you had 4 people each give you x number of apples and you ended up with 12 apples. How many people gave you apples. ( 4x=12). To solve that you would divide the number you ended up with by the number of people that gave you apples. (12/4) and get the number that each person gave you. (x=3)

These types of algebra problems are based on the fact that there are opposites.
multiplication vs division
addition vs subtraction
( I wont go into the properties of inverses and identities that makes this true)
so if you have a number multiplied by x, then you need to divide by it to get x by itself.
if you have x divided by a number you need to multiply by it to get x by itself. (same idea with addition and subtraction. you have to do the opposite of what was done to it.)
so for your problems.

1. -3x=27
you have x multiplied by -3 so you have to divide both sides by -3
-3x/-3 =27/-3
-3/-3 is 1 so you end up with 1x or x on that side
x=-9

2. 3/7 x =15
you have to divide by 3/7 on both sides.
(3/7 x) / (3/7) = 15 / (3/7)
to divide fractions you have to flip the second number (reciprical) and multiply
(3/7) * (7/3) x= 15 * (7/3)
21/21=1 so you only have 1x or just x on that side and on the other side you have 105/3 which equals 35 so
x= 35

Answer 8

1) what times -3 would equal 27. - times - =+, so you need a negative number. Refer back to mulitiplication, 9 times 3 equals 27. so x=-9

another way of thinking about it is to divide both sides of the equation by -3. This makes x by itself on the left side of the equal sign (since -3/-3 =1)

2) is it (3/7)x=15 or 3/(7x)=15? do what it takes to get x on on side of the equation and the rest of the numbers on the other side. Whatever you do to one side of the equation, you do to the other.

Answer 9

Basic algebra. Remember that you have an "equation", meaning both sides of the = symbol are equal, therefore if you perform an operation to one side, then the other, it remains equal. So, in your first equation we have -3x=27, we need to know x, so we need to somehow get rid of the -3. If we divide the left side by -3, then -3x/-3 gives us 1x,or just x (-3/-3=1, right?). now that we've done that, for the other side to be equal, we have to do the same thing, divide by -3. Therefore x=27/-3, which is -9.

Answer 10

1) -3x=27.
x =-9


2) 3/7x=15.?
3 = 15(7x)
x= 3/7(15) = 1/35 .